The invention of quaternions by William Rowan Hamilton marked a significant advancement in mathematics that transcended previous conceptions of complex numbers. Prior to Hamilton's work, mathematics was predominantly grounded in two-dimensional representations. Hamilton sought to extend this framework to accommodate three-dimensional space, leading to the creation of quaternions, represented as a four-dimensional number system. This system consists of one real part and three imaginary parts, providing a powerful tool for representing rotations and orientations in three-dimensional space. The moment of discovery occurred during a contemplative walk along the Royal Canal in Dublin, where Hamilton was struck with inspiration. In a flash of brilliance, he carved the fundamental quaternion formula, Q = a + bi + cj + dk, into the stone of Broom Bridge, embedding the essentials of this new mathematical paradigm into history itself. The introduction of quaternions not only showcased Hamilton's genius but also opened the door for new methods of computation in multiple fields, including physics and engineering. Subsequently, the work on quaternions began to receive attention and recognition, leading to profound implications across various scientific domains, including the study of fluid dynamics, computer graphics, and robotics.